Band-structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz

Understanding the interplay between electronic correlations and band topology remains a central challenge in condensed matter physics, primarily hindered by a language-mismatch problem. While band topology is naturally formulated within a single-particle band theory, strong correlations typically elude such an effective one-body description. In this work, we bridge this gap by leveraging the ghost Gutzwiller (gGut) variational embedding framework, which introduces auxiliary quasiparticle degrees of freedom to recover an effective band-structure description of strongly correlated systems. This approach enables an interpretable and computationally efficient treatment of correlated topological phases, resulting in energy- and momentum-resolved topological features that are directly comparable to experimental spectra. We exemplify the advantages of this framework through a detailed study of the interacting Bernevig-Hughes-Zhang model. Not only does the gGut description reproduce established results, but it also reveals previously inaccessible aspects: most notably, the emergence of topologically nontrivial Hubbard bands hosting their own edge states, as well as possible ways to manipulate these through a finite magnetization. These results position the gGut framework as a promising tool for the predictive modeling of correlated topological materials.